$\begin{array}{l}
\frac{2}{{\sqrt 5 - \sqrt 3 }} + \frac{3}{{\sqrt 6 }} + \sqrt 3 - \sqrt 5 \\
= \frac{{2\left( {\sqrt 5 + \sqrt 3 } \right)}}{{\left( {\sqrt 5 - \sqrt 3 } \right)\left( {\sqrt 5 + \sqrt 3 } \right)}} + \frac{{\sqrt 3 .\sqrt 3 }}{{\sqrt 3 .\sqrt 2 }} + \sqrt 3 - \sqrt 5 \\
= \frac{{2\left( {\sqrt 5 + \sqrt 3 } \right)}}{{5 - 3}} + \frac{{\sqrt 3 }}{{\sqrt 2 }} + \sqrt 3 - \sqrt 5 \\
= \sqrt 5 + \sqrt 3 + \frac{{\sqrt 3 }}{{\sqrt 2 }} + \sqrt 3 - \sqrt 5 \\
= 2\sqrt 3 + \frac{{\sqrt 3 }}{{\sqrt 2 }} = \sqrt 3 \left( {2 + \frac{1}{{\sqrt 2 }}} \right)
\end{array}$
